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gizmo_the_mogwai [7]
3 years ago
7

OC and OR are similar. Find the length of QP.

Mathematics
1 answer:
Elena L [17]3 years ago
5 0

Given:

Circle C and circle R are similar.

The length of arc AB is s = \frac{22 \pi}{9}

The radius of circle C (AC) = 4 unit

The radius of circle R (QR) =6 unit

To find the length of arc QP.

Formula

The relation between s,  r and \theta is

arclength = 2\pi r \frac{\theta}{360}

where,

s be the length of the arc

r be the radius

\theta be the angle.

Now,

For circle C

Taking r = 4

According to the problem,

2 \pi r \frac{\theta}{360} = \frac{22 \pi}{9}

or, 2r \frac{\theta}{360} = \frac{22}{9} [ eliminating \theta from both side]

or, \theta = \frac{(22)(360)}{(9)(2)(4)}

or, \theta = 110^\circ

Again,

For circle R

Taking, r = 6 and \theta = 110^\circ we get,

The length of arc QP is

arc length = 2\pi (6)(\frac{110}{360} )

or, arclength = \frac{11 \pi}{3}

Hence,

The length of QP is \frac{11 \pi}{3}. Option C.

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